It is well known that thermoplastic elastomers, more particularly, thermoplastic block copolymers can be oil-extended to produce soft and flexible compositions. However, the oil plasticized thermoplastic block copolymer compositions of the prior art suffers from one or more of the poor physical and mechanical properties such as poor breaking strength, poor elongation, poor craze, tear, creep, and crack resistance, and poor oil acceptance, to name a few. For instance, Shell Technical Bulletin No. SC 65-75 teaches the use of poly(styrene-ethylene-butylene-styrene) triblock copolymers Shell Kraton G 1650 and G 1652 having styrene end block to ethylene and butylene center block ratio of 28:72 and 29:71 respectively in blends with butyl rubber, tackifier, filler, and oil. However, in none of the blends just described are the properties of the compositions desirable; but rather, the use of other polymers such as butyl rubber, tackifiers, and fillers for extending and plasticizing the triblock copolymers result in dimensionally unstable mastic like materials which are not acceptable for purposes of the present invention. Furthermore, when the triblock copolymers as disclosed in Shell's Bulletin No. SC 65-75 are plasticized with oil, the compositions obtained show decreases in the desired properties such as poor elongation and tensile strength, poor creep, craze, tear, and crack resistance; in addition, these compositions of the prior art tend to rupture and crumble when submitted to moderate shearing stress conditions.